Great! This topic is timely for me as well.
I would like to begin having my students use Sage this year in my high
school calculus class. (The class is roughly equivalent to the first
two semester of a college class. Students will take the AP BC exam
in May and so I have long included the use of a TI-8x calculator.) I
need to assume that students have never programmed and have not heard
of any math software, let alone used something -- even a spreadsheet.
I'd like to have a documentation to take these students from where
they are to having enough Sage at any time in the year to augment
their work in class -- maybe JESTEC
Just Enough Sage To Enhance Calculus
I've set up an experimental Sage server in my basement and have met
with a few students this summer to try out some ideas. Here are
(notes about a possible opening session. I have intentionally stayed
away from the plot command as I want students to build a little
appreciation of what goes into making (and meaning) of a function
graph.
I'm closed with a few lines of (my first effort at) ReStructuredText
which might help. It has occured to me that I might take some Python
and Sage documentation which is in Sphinx and build a set of
documentation of first year calculus students.
Comments and help will be greatly appreciated.
-Bruce
.. Begin ReST
.. _Notes of Introduction to JESTEC:
====
Notes of Introduction to JESTAC (Just Enough Sage To Enhance Calculus):
====
I'd like to get them up and running by looking at lists, math functions, and
list_plots. As these students have taken precalculus, I assume they have
seen sigma notation.
Math Notation to Sage
----
The first step is to go from the math notation of:
$$\sum_{i = 0}^7 i^2$$
to the Sage/Python notation of::
sage: L = [i^2 for i in range(8)]
sage: L
sage: sum(L)
Function Domain, Range and Ordered Pairs
----
Now focus of math functions with a discrete domain and corresponding range::
# introduce a math function
sage: f(x) = x^2
# setup a domain
sage: D = [x for x in range(-4,5)]
# setup a list of ordered pairs
sage: P = [(x,f(x)) for x in D]
sage: P
# plot the ordered pairs
sage: plot1 = list_plot(P);plot1
# setup a domain and range lists
sage: D = [x for x in range(-4,5)]
sage: R = [f(x) for x in D]
# introduce grabbing elements of a list, e.g. the 4th element of R
sage: R[3]
# combine the lists to get the ordered pairs
sage: P1 = [(D[i],R[i]) for i in range(len(D))]
sage: list_plot(P1)
Introduce list where numbers need not be integers
----
(I don't want to get into QQ vs RR.) This also starts students on idea
of named parameters. ::
# Getting more points using non-integer $\Delta x$.
sage: deltax = 0.5
sage: start = -4
sage: stop = 4 + deltax
sage: f(x) = x^2
sage: D2 = [x for x in srange(start,stop,deltax)]
sage: P2 = [(x,f(x)) for x in D2]
sage: plot2 = list_plot(P2)
Use lists to plot parametric functions
----
The need for the *aspect_ratio* parameter comes up naturally::
# lists and parametric functions
sage: x(t) = cos(t) ; y(t) = sin(t)
sage: C = [(x(t),y(t)) for t in srange(0,2*pi,pi/8)]
sage: list_plot(C)
# fix the aspect ratio to get a better circle
sage: list_plot(C,aspect_ratio=1)
.. end ReST
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